Yes, it's possible to use a webcam, but the webcam needs to be attached to PC and installed properly. After its installation, restart Bluestacks and type Camera in the search bar to locate the application. Start it and you should see the video stream. Once you confirm it's working, start KIK and the camera can be used properly.
No other application has to use the application while you attempt to open the video stream in Bluestacks/Kik.